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A149336 Number of walks within N^3 (the first octant of Z^3) starting at (0,0,0) and consisting of n steps taken from {(-1, 0, 0), (-1, 1, 1), (0, -1, 0), (0, 1, -1), (1, 1, 0)} 0
1, 1, 4, 12, 40, 147, 552, 2108, 8316, 33289, 134841, 553959, 2298348, 9612184, 40539298, 172119016, 735000952, 3156525934, 13621846126, 59039338928, 256950972772, 1122435218403, 4919640466189, 21631898475941, 95393882536337, 421809165548347, 1869910737898759, 8309058724349230 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..27.

A. Bostan and M. Kauers, 2008. Automatic Classification of Restricted Lattice Walks, ArXiv 0811.2899.

MATHEMATICA

aux[i_Integer, j_Integer, k_Integer, n_Integer] := Which[Min[i, j, k, n] < 0 || Max[i, j, k] > n, 0, n == 0, KroneckerDelta[i, j, k, n], True, aux[i, j, k, n] = aux[-1 + i, -1 + j, k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[i, 1 + j, k, -1 + n] + aux[1 + i, -1 + j, -1 + k, -1 + n] + aux[1 + i, j, k, -1 + n]]; Table[Sum[aux[i, j, k, n], {i, 0, n}, {j, 0, n}, {k, 0, n}], {n, 0, 10}]

CROSSREFS

Sequence in context: A028403 A149334 A149335 * A149337 A149338 A149339

Adjacent sequences:  A149333 A149334 A149335 * A149337 A149338 A149339

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved

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Last modified December 10 13:27 EST 2016. Contains 279004 sequences.